Considerable attention has been directed toward the development of various types of filters, and especially toward adaptive filters. An adaptive filter is intended to do what its name implies. It is a filter which filters an incoming signal but which adapts or changes its filtering characteristics in accordance with a change of some condition, usually related to the signal being filtered.
There exist many adaptive filter designs, as for example the Kalman filter (based upon what is known as the least mean square criterion), the phase-locked loop, and the adaptive array antenna. Each of these adaptive filters is suited to a particular class of problems. For example, the phase-locked loop adaptively adjusts the frequency of oscillation, and an adaptive antenna places nulls in an antenna pattern to reject sidelobe interference in a changing interfering environment.
The U.S. Pat. No. 3,889,108 to Cantrell, discloses an adaptive filter which is suited for a special class of problems which generally relate to the filtering of a signal to remove higher-order frequency components. It is desirable to remove these high frequency components when they are not related to the true signal but are part of signal noise which causes interference and tends to mask the true signal.
The Cantrell patent discloses an adaptive digital lowpass filter which adaptively changes its bandwidth filtering characteristics in accordance with the bandwidth of the incoming signal. The filter cutoff point may be increased to a higher frequency, or decreased to a lower frequency, by using prior signal inputs and outputs of the filter.
As shown in FIG. 3 of the Cantrell patent, the filter 20 receives an input signal w(k) and outputs an output signal x(k). The operation of the filter is represented by the equation x(k)=w(k) [1-1(k)]+a(k)x(k-1), shown within the filter block 20, where a(k) is an adaptive error signal based on the noise level in the signal. When the noise level increases, a(k) approaches 1.0, and the output signal x(k)=x(k-1). Thus, the immediate past filter output signal is taken as the current filter output signal. Also, as described beginning at column 5, line 55, when there is little noise present, a(k) becomes small, and the input value w(k) appears at the output x(k).
Thus, the Cantrell patent broadly discloses an adaptive digital filter which varies the bandwidth based on prior signal inputs and outputs of the filter while estimating the noise level present in the signal.
In general, fuzzy logic provides procedures to incorporate knowledge expressed vaguely and yet arrive at a definite, calculable answer. In other words, fuzzy logic is a methodology for handling knowledge that contains some uncertainty or vagueness. The foundations of fuzzy logic were set forth in the 1960s by L. A. Zadeh in his paper entitled "Fuzzy Sets", INFORM. CONTR., 8 pp. 338-353, 1965.
In current engineering application, fuzzy logic is most often found in control problems in the form of a particular procedure, called "max-min" fuzzy inference as described by Ebrahim Mamdani in his paper entitled "Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis", IEEE TRANSACTIONS ON COMPUTERS, (1977) C-26, No. 12, pp. 1182-1191. This procedure incorporates approximate knowledge of approximate control response for different circumstances into sets of rules for calculating a particular control action. The rules are expressed in terms of "IF (situation holds), THEN (take consequent control action). The degree to which a particular consequent action is taken depends on the degree to which its corresponding conditions hold. The linguistic expression of a situation or consequent control action is translated into a definite calculation via specified membership functions. A membership function quantifies what is meant by a phrase such as "The temperature is high" by defining the degree of membership in the class, "high", depending on the value of the input variable, temperature.